color(blue)"The equations of motion" are continuous function used to describe objects in movement under the action of one or more forces at constant acceleration affected by the environment too.
Examples:
=>The momentum balance in the x and y directions are:
"∂u/∂t" + "u ⋅ ∇u" − f v = − "∂ϕ/∂x" − ∂/∂ z ( u ′ w ′ − ν ∂u/∂z ) + F_u + D_u
"∂v/∂t" + "v ⋅ ∇v" − f u = − "∂ϕ/∂x" − ∂/∂ z ( v ′ w ′ − ν ∂v/∂z ) + F_v + D_v
=>The time evolution of a scalar concentration field,
C ( x , y , z , t )
=>The equation of state is given by: ρ = ρ ( T , S , P )
=>The continuity equation for an incompressible fluid:
"∂u/ ∂x" + "∂v/∂y" + "∂w/∂z" = 0
=> Any motion equation can be established when a dependent variable will be changing with time, force, space, thermodynamics, or why not gravity fluctuation. Empirical correlations can be established or using the typical motion equations from literature.